U.K.-based start-up bank Monzo will not be bought up by a larger player, its chief executive told CNBC.

"We have no plans to be acquired at all," Tom Blomfield said in an interview last week.

The mobile app-based lender revealed earlier this month that U.S. payments unicorn Stripe was one of several investors to participate in a £71 million ($93 million) funding round. London-based Monzo said it is now worth $366 million following the investment.

Stripe, which was co-founded by Irish brothers Patrick and John Collison in 2010, processes transactions for individuals and businesses.

Blomfield said that advice he and Monzo's other co-founders received from Stripe's executives was "hugely valuable." But he added that he was "very clear" with the Collison brothers on being against a takeover bid.

"I was very clear on this with John and Patrick at Stripe. Their ambition is to build a really, really huge company and ours is the same," he said. Stripe was not immediately available for comment when contacted by CNBC.

Monzo's boss has previously said his fintech (financial technology) firm has been approached by "big banks and big tech companies" offering to acquire it. At the time, Blomfield said "those kinds of acquisitions never really go well."

'Marketplace banking'

Monzo isn't planning on partnering with a major bank any time soon but wants to build a shared "marketplace" ecosystem with them, Blomfield said.

"Where we're going longer term is in marketplace banking, where we're trying to build Monzo into a control center, into a dashboard, a marketplace. So we do the day-to-day money management but say for example you want a mortgage, that's not something we would provide, so actually we'll offer mortgages from other banks on our platform."

The firm is one of many digital challenger banks set up with the aim of competing with larger lenders. Earlier this month another challenger, Revolut, announced it had applied for a European banking license in order to add credit and deposit services to its offering.

More than 400,000 people use Monzo's app, 20,000 of which have set up a current account.

The digital challenger was given a banking license by U.K. regulators earlier this year.